MA151-The World of Numbers: From Euclid to the Information Age
Blocks I & II: Stefan Erickson & John Watkins, MA151, The World of Numbers: From Euclid to the Information Age.
Meets one unit of Natural Science divisional credit and two units Critical Perspectives: The West in Time.
Numbers are as fundamental to humans as are language and music. People have been writing numbers for as long as they have been writing. In this course, we will trace the use of numbers from the ancient civilizations of the Middle East, Egypt, and Mesopotamia, through the axiomatic deductive approach taken by the Greek and Hellenistic civilizations, all the while observing the many influences from around the world from places such as India and medieval Islam, and eventually we will arrive at the end of the twentieth century at the proof of Fermat’s Last Theorem.
The way that people think about numbers has evolved over time: natural numbers, prime numbers, rational numbers, Fibonacci numbers, real numbers, complex numbers. Similarly, our ability to calculate has evolved: the Peruvian quipu, the Chinese abacus, the modern microprocessor. In this course we will consider the impact of computers on today’s society and the role numbers play in search engines and in web security, and we will see how numbers are endlessly useful and endlessly fascinating.
In our historical journey through the development of the mathematics of numbers, we will consider epistemology (What is truth? How do we know what we know?), the role of mathematics in art and architecture (geometry in both classical and modern architecture, as well as perspective in Renaissance art), and the prominence of mathematics in religion (numerology, calendrical systems). We will read primary sources such as Plato and Aristotle, as well as study contemporary plays and films. Along the way we will also delve into the mathematics of other cultures and make comparisons to the Western tradition.
A two-block course taught by one instructor each block; one
grade will be given for the course as a whole.